Fractals: The Math Behind Nature's Patterns

Through researching Thomasina's method of iterating mathematical functions and graphing the result, I have discovered that she was correct in assuming that there are ways of mathematically determining even the most complex patterns in nature. The method that she used is much easier today with new computers which can iterate functions in mere seconds, while it took here much longer doing it by hand in the margins of her math book. When a function is iterated over and over again (that is, each output is put back into the function as a new input) an IFS (Iterative Function Series) fractal is created, which is a self similar, never ending image. Thomasina remarked to Septimus that the equations he had her graph were too industrial, too plain, that for her theory of a formula for nature to be true, there must be something more complicated, and fractals are just that. Patterns in nature that seem too complex to have a mathematical explanation can be explained through fractals, rivers and fjords, canyons, leaves, lightning, and many more seemingly random patterns in nature all fall under the category of fractals.

Here are just a couple:

This website shows many natural fractals with their explanations:
17 Captivating Fractals Found in Nature
Here is a website that explains what a fractal is better than I can:
What are Fractals?

ITW Blog

Assess McCandless' life and death for yourself. Identify and rank the most compelling explanations Krakauer offers, and then explain what you think the story suggests about your/our relationship to nature.

I think that Krakauer puts it best when he admits to seeing some of his younger self in Chris. The whole story about the Stikine ice cap and climbing the devils thumb showed that Krakauer really did share some personality traits with McCandless in that he wanted to prove to himself that he could endure hardship alone in the wilderness, as a means of finding himself. Krakauer wanted to escape from his tedious life in Boulder, CO working as a builder. His trip to Alaska was meant for him to escape into nature, to embrace the challenge of survival on his own, on a walkabout of sorts.  Krakauer talks about how when we are young we have a resistance to settling down into “boring lives,” that we want to do more, and as a way to cope with our indecision, we go off and do things like climb mountains or go on spiritual odysseys like McCandless where we hope to find ourselves.  Krakauer, however, arranged for a food drop and brought equipment that would somewhat ensure his safety, which Chris did not. I think that Chris simply had too much of a flare for the dramatic in him. He was all about speaking his mind through meaningful actions, by completely disappearing from his family and by deciding to go into the wild with little gear and food. Some people think that his fatal flaw was his hubris. That he just didn’t have any mental grasp on his own mortality, but I disagree. I think that he knew exactly what he was getting into, and he liked the fact that there was going to be risk. McCandless loved the drama in symbolic actions, such as burning all the cash in his wallet, or intentionally disobeying laws. This is evident in the postcard he sent to Wayne Westerberg in which he says “If this adventure proves to be fatal and you don’t ever hear from me again I want you to know that you are a great man.”

McCandless' final picure, one of his many actions that come across to me as intentionally dramatic

Chris wouldn’t have it any other way than for there to be a symbolic risk in his adventure, and to acknowledge it in a dramatic one liner in the post card. For Chris, he wanted his relationship to nature to be an authentic one, where he would live off the land with as little gear as possible because that fit into his personality. For Krakauer, although he did almost die several times, he did at least value safety and a little bit of comfort over risk. I agree with McCandless up to a point, and that point is that there is an allure to the wilderness that attracts me, but I don’t agree with taking unnecessary risks in order to have a more “authentic experience.” 

Vine Triptych

I chose to show the irony of my relationship with nature. I do a lot of camping and enjoy spending time in nature, but I still contribute the the destruction of it just like everyone else does. My relationship conflicts with itself in that I appreciate nature as something separate from civilization, but my actions through everyday pollution would seem like I don't appreciate nature. The first two vines show how I take parts of the natural world and bring them into my life, and the last one shows how this appreciation is somewhat false, because my enjoyment of nature is something separate from my everyday polluting life.